Confidence limits studies

Acute toxicity studies are often dominated by consideration of lethaUty, including calculation of the median lethal dose. By routes other than inhalation, this is expressed as the LD q with 95% confidence limits. For inhalation experiments, it is convenient to calculate the atmospheric concentration of test material producing a 50% mortaUty over a specified period of time, usually 4 h ie, the 4-h LC q. It is desirable to know the nature, time to onset, dose—related severity, and reversibiUty of sublethal toxic effects. 

If there is a lack of specific, appropriate data for a process facility, there can be considerable uncertainty in a frequency estimate like the one above. When study objectives require absolute risk estimates, it is customary for engineers to want to express their lack of confidence in an estimate by reporting a range estimate (e.g., 90% confidence limits of 8 X 10 per year to 1 X 10 per year) rather than a single-point estimate (e.g., 2 X 10per year). For this reason alone it may be necessary for you to require that an uncertainty analysis be performed. 

Finally, a 1 1 mixture of acetic and propionic acids containing 2 % of water has been used in order to study the rates of chlorination of polyalkylbenzenes at low temperatures. Second-order rate coefficients were obtained and the values are recorded in Table 58 together with the energies and entropies of activation (which are given with the errors for 95 % confidence limits) from which it was concluded... 

The use of confidence intervals is one way to state the required precision. Confidence limits provide a measure of the variability associated with an estimate, such as the average of a characteristic. Table I is an example of using confidence intervals in planning a sampling study. This table shows the interrelationships of variability (coefficient of variation), the distribution of the characteristic (normal or lognormal models), and the sample frequency (sample sizes from 4 to 365) for a monitoring program. 

Studies in rats reported renal tubular adenomas and adenocarcinomas in male and female animals at doses of 20 mg/kg/day (Kociba et al. 1977a). Metastasis to the lungs was observed. Combined incidences of renal tubular neoplasms in males (9/39, 23%) and in females (6/40, 15%) increased (p <0.05) over controls (males-1/90, females-0/90, 0%). The tumor incidence was not increased in the 0.2 and 2 mg/kg/day dose groups but there were some indications of hyperplasia in animals exposed to 2 m /kg/day. The EPA (1990f) evaluated these data and calculated a human potency factor of 7.8x10 (mg/kg/day) (qi ), representing 95% upper confidence limit of extra lifetime human risk. Based on this value, cancer risk levels of 10, 10, and 10 correspond to exposures of 0.001, 0.0001, 0.00001 mg/kg/day. 

Cost will be the primary controlling factor In the experimental design In essentially all cases. The cost of obtaining the entire population of possible measurements Is prohibitive. The field study design must select a subset which Is representative of the population within definable confidence limits and which can be obtained within the constraints of existing resources. 

Fig. 11. Study of the mobility of valinomycin within a stack of membranes before 0 = 0), immediately after (t = 3 hr) electrodialysis as well as after a five-day period of restacking the membranes 0 = 5 days). c initial ligand concentration Ac, change of total ligand concentration. The size of the circles denotes 95% confidence limits.11 72...

For SK-500 the rate at 573°K and 400 sec after the initiation of reactant flow is independent of reactant mole ratio for Ce C2 = 0.7 to 10. Under these conditions the 400-sec point is just beyond the maximum in the rate curve. Similar behavior was observed at one other condition. Initial rate of reaction estimated by extrapolating the decay portion of the rate curves for this data to zero time (see below) indicates a maximum in the rate at C6 C2 == 3.5 (Figure 2). Error bars represent estimated 95% confidence limits. The observed activity for HY is about twice that of SK-500, that for LaY is about two-thirds that of SK-500 (Figure 2). This is consistent with the trend expected (7) since all catalysts were activated to the same temperature. The temperature dependence of the observed rate is large for all systems studied indicating the absence of external mass transfer limitations. 

Again, the minimum and maximum loading configurations should be studied. Thermocouples will be placed both inside and outside the container at the cool spot location(s), in the steam exhaust line, and in constant-temperature baths outside the chamber. The F0 value will be calculated based on the temperature recorded by the thermocouple inside the container at the coolest area of the load. Upon completion of the cycle, the F0 value will indicate whether the cycle is adequate or if alterations must be made. Following the attainment of the desired time-temperature cycle, cycles are repeated until the user is satisfied with the repeatability aspects of the cycle validation process. Statistical analysis of the F0 values achieved at each repeated cycle may be conducted to verify the consistency of the process and the confidence limits for achieving the desired F0 value. 

In contrast, nominal probability coefficients for chemical carcinogens are derived from upper 95 percent confidence limits of observed responses at high doses, mainly in studies in animals. In some studies, the difference between the upper 95 percent confidence limit and MLE of the observed responses at high doses is an order of magnitude or more. Furthermore, several models have been used to extrapolate the observed responses to the low doses of concern in health protection of the public, with the result that estimated probability coefficients at low doses can differ by several orders of magnitude depending on the extrapolation model chosen. 

For noncarcinogenic hazardous chemicals, NCRP believes that the threshold for deterministic effects in humans should be estimated using EPA s benchmark dose method, which is increasingly being used to establish allowable doses of noncarcinogens. A benchmark dose is a dose that corresponds to a specified level of effects in a study population (e.g., an increase in the number of effects of 10 percent) it is estimated by statistical fitting of a dose-response model to the dose-response data. A lower confidence limit of the benchmark dose (e.g., the lower 95 percent confidence limit of the dose that corresponds to a 10 percent increase in number of effects) then is used as a point of departure in establishing allowable doses. 

In traditional toxicological methods of determining virtually safe doses of hazardous chemicals, nominal thresholds for deterministic responses in humans are estimated based on a NOAEL obtained in human or animal studies. In most high-quality studies, NOAEL is approximately the same as the lower confidence limit of the benchmark dose that corresponds to a 10 percent increase in the number of responses. Thus, as an alternative to the benchmark dose method, the nominal threshold in humans could be set at a factor of 10 or 100 lower than NOAEL obtained in a high-quality human or animal study. However, the benchmark dose method preferred by NCRP... 

The rationale supporting use of EDi0 as the benchmark dose is that a 10 percent response is at or just below the limit of sensitivity in most animal studies. Use of the lower confidence limit of the benchmark dose, rather than the best (maximum likelihood) estimate (EDio), as the point of departure accounts for experimental uncertainty the difference between the lower confidence limit and the best estimate does not provide information on the variability of responses in humans. In risk assessments for substances that induce deterministic effects, a dose at which significant effects are not observed is not necessarily a dose that results in no effects in any animals, due to the limited sample size. NOAEL obtained using most study protocols is about the same as an LED10. 

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